Workshop honoring the 70th birthday of

SCADRON 70Workshop on

"Scalar Mesons and Related Topics"February 11-16, 2008, at IST in Lisbon, Portugal

RECENT ISSUES IN HEAVY-LIGHT MESON SPECTROSCOPY

RECENT ISSUES IN HEAVY-LIGHT MESON SPECTROSCOPY

Francisco Fernández

University of Salamanca

• Light – Heavy quark mesons are hydrogenic atoms of QCD– Heavy Quark limit static colour field &

decoupling of light degrees of freedom– Light quarks characterized by their total angular

momentum jq = sq + L

– jq is combined with SQ to give total angular momentum

– SQ and jq are separately conserved

• In Heavy Quark Limit, each energy level has pair of degenerate states :

Qs

Lsj qq

Q qJ s j

jq=1/2 J=0 D/B

J=1 D*/ B*

L=0jq=1/2 J=0,1 B0

*, B1*

jq=3/2 J=1,2 B1, B2*

L=1 states, also known as B*

D1, D2*

D0*, D1

*

B** Spectroscopy

B1 and B2* decay through D-wave narrow resonances

B0* and B1* decay through S-wave wide resonances, difficult to distinguish from phase space

jq JP Bs* Decay Width

1/2 0+Bs

0

BK Broad (S-wave)

1/2 1+ Bs1* B*K Broad (S-wave)

3/2 1+ Bs1 B*KNarrow (D-

wave)

3/2 2+ Bs2* BK, B*K

Narrow (D-wave)

B** Spectroscopy

Recent experimental

results

New States - DsJ(2860)+, X(2690)+ (?)

• New resonance at 2.86 GeV/c2 • Broad state at 2.69 GeV/c2

DsJ(2860)+

invariant mass (GeV/c2)

Combined modes bkgd subtracted

Ds2573)+

D0 K-+D0 K-+ 0 D+ K-++

BaBar data PRL 97 (2006)

No structures seen in D*K

BB++→→DD00DD00KK++

J=0 2/ndf = 185/5J=1 2/ndf = 7/5 J=2 2/ndf = 250/5

JP = 1-

■ ψ(4160) reflection

Spin Analysis

BELLE data arXiv 0707.3941

DSJ*(2317)

BaBar: PRL 90, 242001 (2003)

•Narrow peak in DS0. JP=0+ I=0 favored.

•Width consistent with the detector resolution, less than 10 MeV.

•Mass near 2317 MeV, 40 MeV below DK threshold.

DSJ (2460)

•Narrow peak in D*S0,

and also observed in DS. JP=1+ favored.

•Width consistent with the detector resolution, less than 8 MeV.

•Mass close to 2460 MeV, below D*K threshold.

CLEO: PRD 68, 032002 (2003)

Meson Mass JP

DsJ*(2317) m=(2319.6 ± 0.2 ± 1.4) MeV/c2

0+

DsJ*(2460) m=(2460.1± 0.2 ± 0.8) MeV/c2

1+

Ds1*(2535) m=(2535.3± 0.6 ± 1.4) MeV/c2

1+

Ds2*(2572) m=(2572.2± 0.3 ± 1.0) MeV/c2

2+

DsJ*(2860) m=(2856.6± 1.5 ± 5.0) MeV/c2

?

DsJ*(2700) m=(2715± 11 +11-14 ) MeV/c2 1-

Summary

Excited B Mesons (B1, B2*)

Excited B Mesons (B1, B2*)

CDF Run II

B1 B*+, B2* B*+, B2* B+

Excited B Mesons (B1, B2*)

DØ 1 fb-1

DØ Run II

Orbitally Excited Bs-mesons

Bs2*

Bs1

MODELS

QUARK MODELS

MOST OF THESE STATES PRESENT UNEXPECTED PROPERTIES QUITE DIFFERENT FROM THOSE PREDICTED BY

THE STANDARD QUARK POTENTIAL MODELS IF A PURE CONFIGURATION IS CONSIDERcq

_

Modification are needed

Matsuki: Semirelativistic potential model

Talk on Friday

One loop corrections to the Fermi-Breit interaction

→ →

→

JP=0+

CONFIGURATIONcq_

Strong coupling with the nearby S wave DK channel

JP=0+

JP=3-

Salamanca model

Vijande, Valcarce

Constituent Quark Model

Generalization to heavy flavours of the original SU(2)F model developed in J. Phys. G19 2013 (1993)

Basic ingredients•Chiral symmetry is spontaneously broken at some momentum scale provinding a constituent quark mass M(q2) for the ligth quarks

• As a consecuence light constituent quarks exchange Goldstone bosons

•Both light and heavy quarks interacts besides by gluon exchange

•Finally both type of quarks are confined by a two body linear potential screened at large distancies due to pair creation

Details can be found in J. of Phys. G: Nucl. Part Phys. 31 1-26

• N-N interaction– F. Fernández, A. Valcarce, U. Straub, A. Faessler. J. Phys. G19, 2013 (1993)– A. Valcarce, A. Faessler, F. Fernández. Physics Letters B345, 367 (1995)– D.R. Entem, F. Fernández, A. Valcarce. Phys. Rev. C62 034002 (2000)– B. Juliá-Diaz, J. Haidenbauer, A. Valcarce, and F. Fernández. Physical

Review C 65, 034001, (2002)

• Baryon spectrum– H. Garcilazo, A. Valcarce, F. Fernández. Phys. Rev. C 64, 058201, (2001)– H. Garcilazo, A. Valcarce, F. Fernández. Phys. Rev. C 63, 035207 (2001)

• Meson spectrum.– L.A. Blanco, F. Fernández, A. Valcarce. Phys. Rev. C59, 428 (1999)– J. Vijande, F. Fernández, A. Valcarce. J. Phys. G31, (2005)

Constituent Quark Model

Deuteron

NN phase shifts

Triton

Constituent Quark Model

Meson spectra (I)

0

2 0 0

4 0 0

6 0 0

8 0 0

1 0 0 0

1 2 0 0

1 4 0 0

1 6 0 0

1 8 0 0

2 0 0 0

E (

MeV

)

0 -+ 2 -+ (1 --) 3 -- b 1(1 + -) a 2(2 + +) a 1(1 + +)

Light I=1

Meson spectra (VI)

9 2 0 0

9 4 0 0

9 6 0 0

9 8 0 0

1 0 0 0 0

1 0 2 0 0

1 0 4 0 0

1 0 6 0 0

1 0 8 0 0

11 0 0 0

11 2 0 0

E (

MeV

)

b(0 -+ ) (1 --) b 0(0 + + ) b 1(1 + +) b 2(2 + + ) (2 --)

Bottomonium

L=1

Why four quarks configuration?

qqqq

csJπ=0+,1+

L=0

P( s )=-1−

→

→P(qq)=+1−

−

TETRAQUARKS

Numerical techniques

4q

3q1q

2qx y

z

The two-body problem is solved using the Numerov algorithm.

The four-body problem (two particles and two antiparticles) is solved by means of a variational method.

Three main difficulties:• Non-trivial color structure.

• Symmetry properties in the radial wave function (Pauli Principle)

• Two- and four-body mixing.

2q

1q

r +

3 3 3 8 8 101Baryon

6 6 8 27

6

1

3 8 10

3 6 8 103 3 3 3

3 3 1 8

Tetraquark

3 3 81Meson

•Non-trivial color structure.

Four-Body formalism

1 2!

We expand the radial wave function in terms of generalized gaussians with

-Well defined permutation properties (SS, AA, AS, SA).- L= 0 (relative angular momenta li 0)- Positive parity

•Symmetry properties in the radial wave function (Pauli Principle)

Four-Body configurations.

1 2| 0 | |B qq qqqq

q

q

q

q

q

q s

s

q

q

s

s

qC

• Two- and four-body mixing

nncnncD

nscnscD

nscnscD

J

SJ

SJ

33*

22

11*

)2308(

)2460(

)2317(

0 1

0 0,

0 0

qq

qqqq

H wH H

H w

0 1H H H

Quark model predictions

→

→

←

DECAY WIDTHS

Γ[DsJ(2860)0+ → Ds*γ] = 13.67 keV

Γ[DsJ(2860)0+ → Ds*γ] = 1.8 eV

multiquark

2P radial excitation

B meson sector

B meson sector

B meson sector

B meson sector

Below BK and B*K thresholds

→ →

→

Above Bπ threshold

M(B0*)=5658 MeV

M(B1) =5756 MeV

Back to the L3 Collaboration

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Thank you